How do you factor by grouping 3x^2 - 17x + 10?

2 Answers
Shwetank Mauria
Aug 10, 2018

3x^2-17x+10=(3x-2)(x-5)

Explanation:

In the quadratic polynomial 3x^2-17x+10, the coefficient of x^2 and constant term are of same sign and their product is 30,

hence we should split -17, the coefficient of x. in two parts, whose sum is 17 and product is 30. These are 2 and15 and hence

3x^2-17x+10

= 3x^2-15x-2x+10

= 3x(x-5)-2(x-5)

= (3x-2)(x-5)

Note - If sign of coefficient of x^2 and constant term are different, find two numbers whose difference is equal to the coefficient of x.

Jim G.
Aug 10, 2018

(x-5)(3x-2)

Explanation:

"factor the quadratic using the a-c method"

"the factors of the product "3xx10=30

"which sum to "-17" are "-15" and "-2

"split the middle term using these factors"

3x^2-15x-2x+10larrcolor(blue)"factor by grouping"

=color(red)(3x)(x-5)color(red)(-2)(x-5)

"take out the "color(blue)"common factor "(x-5)

=(x-5)(color(red)(3x-2))

3x^2-17x+10=(x-5)(3x-2)

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